Robustness of spatialpreferentialattachment networks

Peter Mörters (Bath)
Wednesday, November 18, 2015 - 6:15pm
WIAS, Erhard-Schmidt-Saal, Mohrenstraße 39, 10117 Berlin

A growing family of random graphs is called robust if it retains a giant component after percolation with arbitrarily small positive retention probability. We study robustness for graphs, in which new vertices are given a spatial position on the unit circle and are connected to existing vertices with a probability favouring short spatial distances and high degrees. In this model of a scale-free network with clustering we can independently tune the power law exponent \tau of the degree istribution and the exponent \delta at which the connection probability decreases with the distance of two vertices. We show that the network is robust if \tau < 2 + 1/\delta, but fails to be robust if \tau > 2 + 1/(\delta − 1). This is the first instance of a scale-free network where robustness depends not only on its degree distribution but also on its clustering features. This is joint work with Emmanuel Jacob (ENS Lyon).